Herman Cain told key staff and volunteers Tuesday that he is reassessing the future of his presidential candidacy. Photo: AP

WASHINGTON — Herman Cain told key staff Tuesday he is reassessing the future of his presidential candidacy in the wake of an allegation that he carried on a 13-year affair with an Atlanta woman.

Cain told campaign staff on a Tuesday morning conference call that the allegations may create “too much of a cloud, in some people’s minds, as to whether or not they would be able to support us going forth,” according to National Review Online (NRO), which was on the call.

“The public will have to decide whether they believe her or whether they believe me,” Cain said. “That’s why we’re going to give it time, to see what type of response we get from our supporters.”

“If a decision is made different than to plow ahead, you all will be the first to know,” he said, according to NRO.

The woman, Ginger White, told WAGA-TV she had an extended, sexual relationship with Cain after meeting him in the late 1990s at an event he attended in his former role as president of the National Restaurant Association.

White, who presented cell phone records as evidence of their frequent contact, said her physical relationship with Cain ended about eight months ago — before Cain announced he was running for president — but that her friendship with the candidate had continued.

Before the interview aired Monday evening, Cain preemptively denied White’s claims during an appearance on CNN. Later, he released a statement suggesting her story was another example of “dirty politics and smear tactics” and evidence some people are “afraid of a Cain presidency.”

“My plan is to continue to spread my vision on how I would renew America and keep her safe,” he said in the statement.

During the conference call, Cain said he would give a foreign policy speech at Hillsdale College in Michigan Tuesday evening as planned and promised to “deliver it with vim, vigor and enthusiasm,” NRO reported.

Cain also continued to deny the affair allegations, saying he had considered White a friend and had tried to help her financially.

He acknowledged, however, that White’s claims had taken a toll on his family and his wife of 43 years, Gloria.

There were other signs Tuesday that Cain’s campaign has been badly rattled by the new allegations.

NY1 News reported that Cain abruptly canceled Tuesday morning a private dinner at the Park Avenue home of New York Post gossip columnist Cindy Adams, which was planned for Sunday evening to introduce the candidate to members of New York’s media elite.

The guest list for the dinner also included Barbara Walters, Matt Lauer, Bill O’Reilly and Greta Van Susteren, NY1 reported.

According to Politico, Cain is also reaching out to his supporters individually for their advice on how his campaign should proceed following this new report.

The bombshell came weeks after the former pizza magnate’s campaign was set back by allegations of sexual harassment, which he also firmly denied.

Although the latest report involves an alleged consensual relationship, the claims may further weaken Cain’s support among conservative Republicans concerned about social issues, including the institution of marriage.